Bifurcation study of azimuthal bulk flow in annular combustion systems with cylindrical symmetry breaking

In annular combustion systems, azimuthal thermoacoustic modes manifest themselves predominantly as travelling or standing waves. Several phenomena can influence the modal behaviour of annular thermoacoustics. To monitor the stability of azimuthal thermoacoustics in industrial installations, a better understanding of the dynamics is required to correctly interpret online measurements. In this work, thermoacoustic eigensolutions of annular combustion systems are investigated, using a low-order analytic model. Heat release fluctuations are considered as a weak source term for a given acoustic eigenmode. The fluctuating heat release is modelled as a linear feedback to the local acoustics, in which the feedback response is a function of the azimuthal coordinate, causing cylindrical symmetry breaking. A bifurcation map is generated as a function of azimuthal mean flow velocity around the annulus. It is shown that a pitchfork bifurcation exists, separating standing wave and travelling wave solutions. Due to the interaction with non-uniform thermoacoustic feedback, an azimuthal flow with a low Mach number can significantly influence the system stability. Close to the bifurcation point, the non-normal nature of the dynamic system can induce a considerable gain of acoustic energy and yield more predictable time traces. These findings address the influence of non-normality, when applying a linear damping rate, acoustic amplitude or entropy-based quantity with the intent to monitor combustion dynamics in an annular combustion system.